Heat Kernel on Lie Groups and Maximally Symmetric Spaces / by Ivan G. Avramidi.

Format:

Book

Author/Creator:

Avramidi, Ivan G., 1957- author.

Series:

Frontiers in Mathematics, 1660-8054

Language:

English

Subjects (All):

Global analysis (Mathematics).

Manifolds (Mathematics).

Differential equations.

Mathematical physics.

Group theory.

Global Analysis and Analysis on Manifolds.

Differential Equations.

Mathematical Physics.

Group Theory and Generalizations.

Local Subjects:

Global Analysis and Analysis on Manifolds.

Differential Equations.

Mathematical Physics.

Group Theory and Generalizations.

Physical Description:

1 online resource (197 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2023.

Summary:

This monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form – and derives them – for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics – such as global analysis, spectral geometry, stochastic processes, and financial mathematics – as well in areas of mathematical and theoretical physics – including quantum field theory, quantum gravity, string theory, and statistical physics.

Contents:

Part I. Manifolds

Chapter. 1. Introduction

Chapter. 2. Geometry of Simple Groups

Chapter. 3. Geometry of SU(2)

Chapter. 4. Maximally Symmetric Spaces

Chapter. 5. Three-dimensional Maximally Symmetric Spaces

Part II: Heat Kernel

Chapter. 6. Scalar Heat Kernel

Chapter. 7. Spinor Heat Kernel

Chapter. 8. Heat Kernel in Two Dimensions

Chapter. 9. Heat Kernel on S3 and H3

Chapter. 10. Algebraic Method for the Heat Kernel

Appendix A

References

Index.

Notes:

Includes bibliographical references and index.

Other Format:

Print version: Avramidi, Ivan G. Heat Kernel on Lie Groups and Maximally Symmetric Spaces

ISBN:

9783031274510

OCLC:

1377816879